A126845 Ramanujan numbers (A000594) read mod 23.

1, 22, 22, 0, 0, 1, 0, 1, 0, 0, 0, 0, 22, 0, 0, 22, 0, 0, 0, 0, 0, 0, 1, 22, 1, 1, 1, 0, 22, 0, 22, 0, 0, 0, 0, 0, 0, 0, 1, 0, 22, 0, 0, 0, 0, 22, 22, 1, 1, 22, 0, 0, 0, 22, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 22, 0, 22, 0, 22, 0, 22, 0, 0, 22, 0, 0, 22, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0

Offset

1,2

References

G. H. Hardy, Ramanujan, Twelve Lectures on Subjects Suggested by His Life and Work, Cambridge, 1940, p. 166.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.

Formula

a(n) = 0 if Legendre symbol (n,23) = A011586(n) = -1 (Hardy, 1940). - Amiram Eldar, Jan 04 2025

Mathematica

a[n_] := Mod[RamanujanTau[n], 23]; Array[a, 100] (* Amiram Eldar, Jan 04 2025 *)

Prog

(PARI) a(n) = ramanujantau(n) % 23; \\ Amiram Eldar, Jan 04 2025

Crossrefs

Cf. A000594, A011586.

Sequence in context: A291491 A022978 A023464 * A350086 A361686 A010861

Adjacent sequences: A126842 A126843 A126844 * A126846 A126847 A126848

Keyword

nonn

Author

N. J. A. Sloane, Feb 25 2007

Status

approved